CN110601678B - Method and device for realizing zero phase of IIR filter - Google Patents

Method and device for realizing zero phase of IIR filter Download PDF

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CN110601678B
CN110601678B CN201910819813.6A CN201910819813A CN110601678B CN 110601678 B CN110601678 B CN 110601678B CN 201910819813 A CN201910819813 A CN 201910819813A CN 110601678 B CN110601678 B CN 110601678B
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filter
signal
zero phase
phase
iir
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CN110601678A (en
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余惠雄
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Huizhou Desay SV Intelligent Transport Technology Research Institute Co Ltd
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Huizhou Desay SV Intelligent Transport Technology Research Institute Co Ltd
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0202—Two or more dimensional filters; Filters for complex signals
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0283—Filters characterised by the filter structure
    • H03H17/0286—Combinations of filter structures
    • H03H17/0288—Recursive, non-recursive, ladder, lattice structures
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H2017/0072—Theoretical filter design
    • H03H2017/009—Theoretical filter design of IIR filters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

Abstract

The application relates to a method for realizing zero phase of an IIR filter and a device thereof, which are applied to a device provided with a first filter and a second filter, wherein the method comprises the following steps: inputting the continuous signal into the first filter for filtering to generate a first filtering signal; inputting the first filtering signal to the second filter for filtering, and generating and outputting a second filtering signal with zero phase; wherein the phases of the first filter and the second filter are symmetric up and down along the X axis. The beneficial effects are that: the problem of phase distortion caused by nonlinear phase of an IIR filter is solved, the problem of phase distortion of an acoustic frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal.

Description

Method and device for realizing zero phase of IIR filter
Technical Field
The application relates to the technical field of audio and video signal processing, in particular to a method and a device for realizing zero phase of an IIR filter.
Background
At present, the frequency divider of the sound equipment can generate phase shift, so that the harmonic wave and fundamental wave of music are different in phase, some details of the music can be lost, and the fidelity is affected. Patent application No. 2007100755694, "zero-phase implementation method of IIR filter and zero-phase IIR filter device", requires that an input signal is divided into N blocks, and then backward filtering is performed to perform phase correction and then forward filtering. Another patent application No. 2013106755763, "a digital filtering processing method of an online zero-phase shift IIR digital filter", is similar, and is complex, time-delayed, distorted and limited in accuracy; is not suitable for real-time processing of audio and video continuous signals.
Disclosure of Invention
In order to solve the above technical problems, the present application provides a method for implementing zero phase of an IIR filter, which is applied to a device provided with a first filter and a second filter, and the method includes:
inputting the continuous signal into the first filter for filtering to generate a first filtering signal;
inputting the first filtering signal to the second filter for filtering, and generating and outputting a second filtering signal with zero phase;
wherein the phases of the first filter and the second filter are symmetric up and down along the X axis.
Alternatively, when the first filter is a low-pass filter, the second filter may be a low-pass filter or an all-pass filter.
Alternatively, when the first filter is a high pass filter, the second filter may be a high pass filter or an all pass filter.
Optionally, the first filter and the second filter comprise at least one addition operation, at least one amplification operation, and at least one delay operation.
Optionally, the transfer function of the first filter is:
wherein a1, a2, b0, b1, b2 are coefficients of the first filter.
Optionally, the transfer function of the second filter is:
wherein c1, c2, d0, d1, d2 are coefficients of the second filter.
Optionally, the first filter and the second filter are IIR filters.
In addition, the application also provides a device for realizing zero phase of the IIR filter, which comprises a first filter and a second filter, wherein the device is used for: the input signal is transmitted into the first filter for filtering, and a first signal is generated; and transmitting the first signal into the second filter for filtering to generate a second signal.
Optionally, the first filter and the second filter each include at least one adder, at least one amplifier, and at least one delay.
The application relates to a method and a device for realizing zero phase of an IIR filter, which have the beneficial effects that: the problem of phase distortion caused by nonlinear phase of an IIR filter is solved, the problem of phase distortion of an acoustic frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal. The application has simple structure, convenient implementation, low delay, real-time response of continuous signals, accurate phase compensation and ideal zero phase shift effect, and hardware requirements can support a direct II type IIR filter. Compared with the existing DSP digital signal frequency divider, the application has the advantages that the added calculated amount is not large, and the calculated amount of at most one second-order IIR filter is added, so that the calculated amount is extremely low. The application can also be used for audio and video signal processing, and other signal processing sensitive to phase.
Drawings
FIG. 1 is a signal flow diagram through a first filter and a second filter according to an embodiment of the present application;
fig. 2 is a schematic structural diagram of a first filter and a second filter according to an embodiment of the present application;
FIG. 3 is a Bode diagram of a first filter as a first order low pass filter according to an embodiment of the present application;
FIG. 4 is a Bode diagram of a second filter as a first order low pass filter according to an embodiment of the present application;
FIG. 5 is a Bode plot of the output signal from the first filter and the second filter according to an embodiment of the present application;
wherein F1-first filter, F2 second filter.
Detailed Description
The preferred embodiments of the present application will be described in detail below with reference to the attached drawings so that the advantages and features of the present application will be more readily understood by those skilled in the art, thereby more clearly defining the scope of the present application.
In the embodiment shown in fig. 1, the present application proposes a method for implementing zero phase of an IIR filter, applied to a device provided with a first filter and a second filter, the method comprising:
inputting the continuous signal into a first filter for filtering to generate a first filtered signal;
inputting the first filtering signal into a second filter for filtering, and generating and outputting a second filtering signal with zero phase;
wherein the phases of the first filter and the second filter are symmetric up and down along the X-axis.
In one implementation of the present embodiment, the continuous signal that is continuously input is filtered by the first filter and the second filter. The problem of phase distortion caused by nonlinear phase of an IIR filter is solved, the problem of phase distortion of an acoustic frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal. The application has simple structure, convenient implementation, low delay, real-time response of continuous signals, accurate phase compensation and ideal zero phase shift effect, and hardware requirements can support a direct II type IIR filter. Compared with the existing DSP digital signal frequency divider, the application has the advantages that the added calculated amount is not large, and the calculated amount of at most one second-order IIR filter is added, so that the calculated amount is extremely low. The application can also be used for audio and video signal processing, and other signal processing sensitive to phase.
In some embodiments, when the first filter is a low pass filter, the second filter may be a low pass filter or an all pass filter.
In one implementation of this embodiment, the first filter is a low pass filter and the second filter is a low pass filter; the first filter and the second filter allow low-frequency or direct-current components in the signals to pass through, and inhibit high-frequency components or interference and noise to play a role in filtering.
In another implementation of this embodiment, the first filter is a low-pass filter, and the second filter is an all-pass filter, and since the first filter allows low-frequency or direct-current components in the signal to pass, high-frequency components or interference and noise are suppressed; the second filter is in the full band range, the amplitude of the signal does not change, i.e. the gain in amplitude is constant equal to 1 in the full band. The phase shift is typically performed by an all-pass filter, i.e. the phase of the input signal is changed, ideally the corresponding change in phase shift and frequency is exactly symmetrical to the phase shift of the first filter in the X-axis. After the continuous signal is filtered by the first filter, the high frequency component of the signal is filtered, and the low frequency or direct current in the rest signal is only phase-shifted by the second filter.
In some embodiments, when the first filter is a high pass filter, the second filter may be a high pass filter or an all pass filter.
In one implementation of this embodiment, the first filter is a high-pass filter and the second filter is a high-pass filter; the first filter and the second filter allow high-frequency components in the signals to pass through and inhibit low-frequency or direct-current components.
In another implementation of this embodiment, the first filter is a high pass filter, and the second filter is an all pass filter, and since the first filter allows high frequency components in the signal to pass, low frequency or direct current components are suppressed; the second filter is in the full band range, the amplitude of the signal does not change, i.e. the gain in amplitude is constant equal to 1 in the full band. The phase shift is typically performed by an all-pass filter, i.e. the phase of the input signal is changed, ideally the corresponding change in phase shift and frequency is exactly symmetrical to the phase shift of the first filter in the X-axis. After the continuous signal is filtered by the first filter, the low frequency or direct current component of the signal is filtered, and the high frequency component in the residual signal is only phase-shifted by the second filter.
In some embodiments, referring to fig. 2, the first filter and the second filter include at least one addition operation, at least one amplification operation, and at least one delay operation.
In one implementation of this embodiment, the first filter and the second filter are identical in structure, and the same structure uses different coefficients; in this embodiment, the first filter and the second filter have a structure including 4 adders, 2 retarders, and 5 amplifiers, and the connection relationship between the adders, the retarders, and the amplifiers is as shown in fig. 2.
In some embodiments, the transfer function of the first filter is:
wherein a1, a2, b0, b1, b2 are coefficients of the first filter.
In one implementation of this embodiment, the connection relationship of the adder, the delay and the amplifier is as shown in fig. 2; the structure of the first filter comprises 4 adders, 2 delays and 5 amplifiers; the coefficients a1, a2, b0, b1, b2 affect not only the phase but also the amplitude, and also the filter properties, such as low-pass, high-pass, band-pass, all-pass, band-reject, etc. filters; is an important component of the filter.
In some embodiments, the transfer function of the second filter is:
wherein c1, c2, d0, d1, d2 are coefficients of the second filter.
In one implementation of this embodiment, the connection relationship of the adder, the delay and the amplifier is as shown in fig. 2; the structure of the second filter comprises 4 adders, 2 delays and 5 amplifiers; the coefficients c1, c2, d0, d1, d2 affect not only the phase but also the amplitude, and also the filter properties such as low-pass, high-pass, band-pass, all-pass, band-reject, etc. filters; is an important component of the filter.
In one implementation of the foregoing embodiment, the first filter is a low-pass filter, and the second filter is a low-pass filter corresponding to the "image phase" of the first filter, where the image phase is in this embodiment that the first filter and the second filter use the X-axis of the zero-degree phase as a mirror, and the phases are symmetrical up and down, that is, the phases of the first filter and the second filter are symmetrical up and down along the X-axis.
In the present embodiment, the calculation formulas of the coefficients of the first-order low-pass filter F1 and the first-order low-pass mirror phase filter F2 are as follows:
a 1 = -(1-sinω0+cosω0) / (1+sinω0+cosω0);
a 2 = 0;
b 0 = sinω0 / (1+sinω0+cosω0) ;
b 1 = sinω0 / (1+sinω0+cosω0);
b 2 = 0;
c 1 = -(1+sinω0+cosω0) / (1-sinω0+cosω0);
c 2 = 0;
d 0 = -sinω0 / (1-sinω0+cosω0);
d 1 = -sinω0 / (1-sinω0+cosω0);
d 2 = 0;
wherein ,ω0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
In the present embodiment, at the first order low pass first filter with a cutoff frequency of 1000Hz, the coefficients of the first filter at the sampling frequency fs=48 kHz are:
a 1 = -0.876976462993;
a 2 = 0;
b 0 = 0.061511768504;
b 1 = 0.061511768504;
b 2 = 0;
coefficients of F2:
c 1 = -1.140281458168;
c 2 = 0;
d 0 = -0.070140729084;
d 1 = -0.070140729084;
d 2 = 0;
the baud plot of the first filter, fig. 3, the baud plot of the second filter, fig. 4, and the baud plot of the final signal output, fig. 5.
As shown in fig. 5, the amplitude-frequency characteristic of the output signal is the characteristic of a second-order low-pass filter, is the superposition effect of two first-order low-pass filters, and the phase-frequency characteristic is a straight line with zero phase; the application solves the problem of phase distortion caused by nonlinear phase of the IIR filter, solves the problem of phase distortion of the audio frequency divider, and solves the problem of phase distortion of audio and video signal processing. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal. The application has simple structure, convenient implementation, low delay, real-time response of continuous signals, accurate phase compensation and ideal zero phase shift effect, and hardware requirements can support a direct II type IIR filter. Compared with the existing DSP digital signal frequency divider, the application has the advantages that the added calculated amount is not large, and the calculated amount of at most one second-order IIR filter is added, so that the calculated amount is extremely low. The application can also be used for audio and video signal processing, and other signal processing sensitive to phase.
In one implementation of the foregoing embodiment, the first filter is a low-pass filter, and the second filter is a low-pass filter corresponding to the "image phase" of the first filter, where the image phase is in this embodiment that the first filter and the second filter use the X-axis of the zero-degree phase as a mirror, and the phases are symmetrical up and down, that is, the phases of the first filter and the second filter are symmetrical up and down along the X-axis.
The coefficients, a2, b2, c2, d2, for the second order low pass filter F1 and the second order low pass mirror phase filter F2 are not zero; higher order filters are implemented using a cascade of second order IIR filters.
In one implementation of the foregoing embodiment, the first filter is a high-pass filter, and the second filter is a high-pass filter corresponding to the "image phase" of the first filter, where the image phase is in this embodiment that the first filter and the second filter use the X-axis of the zero-degree phase as a mirror, and the phases are symmetrical up and down, that is, the phases of the first filter and the second filter are symmetrical up and down along the X-axis.
In the present embodiment, the calculation formulas of the coefficients of the first-order high-pass filter F1 and the first-order high-pass mirror phase filter F2 are as follows:
a 1 = -(1-sinω0+cosω0) / (1+sinω0+cosω0);
a 2 = 0;
b 0 = (1+ cosω0) / (1+sinω0+cosω0) ;
b 1 = -(1+ cosω0) / (1+sinω0+cosω0);
b 2 = 0;
c 1 = -(1+sinω0+cosω0) / (1-sinω0+cosω0);
c 2 = 0;
d 0 = (1+ cosω0) / (1-sinω0+cosω0);
d 1 = -(1+ cosω0) / (1-sinω0+cosω0);
d 2 = 0;
wherein ,ω0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
In this embodiment, the first filter and the second filter of the high-pass filter are used, and the phase frequency characteristics thereof form a straight line with a phase of zero degrees after passing through the first filter and the second filter. The application solves the problem of phase distortion caused by nonlinear phase of the IIR filter, solves the problem of phase distortion of the audio frequency divider, and solves the problem of phase distortion of audio and video signal processing. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal. The application has simple structure, convenient implementation, low delay, real-time response of continuous signals, accurate phase compensation and ideal zero phase shift effect, and hardware requirements can support a direct II type IIR filter. Compared with the existing DSP digital signal frequency divider, the application has the advantages that the added calculated amount is not large, and the calculated amount of at most one second-order IIR filter is added, so that the calculated amount is extremely low. The application can also be used for audio and video signal processing, and other signal processing sensitive to phase.
In some embodiments, the first filter, the second filter are IIR filters; in this embodiment, the IIR filter is a recursive filter with feedback. The system function of the IIR filter may be a closed function, and in this embodiment, the structure of the IIR filter is composed of basic operations such as a delayer, an adder, and an amplifier, and the IIR filter may be combined into four structural forms of a direct type, an accurate type, a cascade type, and a parallel type, which all have feedback loops.
In some embodiments, referring to fig. 1, the present application further provides an apparatus for implementing zero phase of an IIR filter, including a first filter and a second filter, where the apparatus is configured to: the input signal is transmitted into a first filter for filtering, and a first signal is generated; and transmitting the first signal into a second filter for filtering to generate a second signal. The first filter and the second filter each comprise at least one adder, at least one amplifier and at least one delayer. In this embodiment, the first filter and the second filter have a structure including 4 adders, 2 retarders, and 5 amplifiers, and the connection relationship between the adders, the retarders, and the amplifiers is as shown in fig. 2. The application solves the problem of phase distortion caused by nonlinear phase of the IIR filter, solves the problem of phase distortion of the audio frequency divider, and solves the problem of phase distortion of audio and video signal processing. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift is achieved in the effective bandwidth of the signal. The application has simple structure, convenient implementation, low delay, real-time response of continuous signals, accurate phase compensation and ideal zero phase shift effect, and hardware requirements can support a direct II type IIR filter. Compared with the existing DSP digital signal frequency divider, the application has the advantages that the added calculated amount is not large, and the calculated amount of at most one second-order IIR filter is added, so that the calculated amount is extremely low. The application can also be used for audio and video signal processing, and other signal processing sensitive to phase.
Finally, it should be noted that: the above examples are only specific embodiments of the present application, and are not intended to limit the scope of the present application, but it should be understood by those skilled in the art that the present application is not limited thereto, and that the present application is described in detail with reference to the foregoing examples: any person skilled in the art may modify or easily conceive of the technical solution described in the foregoing embodiments, or perform equivalent substitution of some of the technical features, while remaining within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (8)

1. A method for implementing zero phase by an IIR filter, applied to a device provided with a first filter and a second filter, the method comprising:
inputting the continuous signal into the first filter for filtering to generate a first filtering signal;
inputting the first filtering signal to the second filter for filtering, and generating and outputting a second filtering signal with zero phase;
wherein the phases of the first filter and the second filter are symmetrical up and down along the X axis,
the transfer function of the first filter is:
wherein a1= - (1-sin ω0+cos ω0)/(1+sin ω0+cos ω0);
a 2 = 0；
b 0 = sinω0 / (1+sinω0+cosω0)；
b 1 = sinω0 / (1+sinω0+cosω0)；
b 2 = 0，
wherein ,ω0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
2. The method for implementing zero phase by IIR filter according to claim 1, wherein when the first filter is a low-pass filter, the second filter may be a low-pass filter or an all-pass filter.
3. The method for implementing zero phase by IIR filter according to claim 1, wherein when the first filter is a high pass filter, the second filter may be a high pass filter or an all pass filter.
4. The method of implementing zero phase for an IIR filter of claim 1 wherein the first filter and the second filter operations comprise at least one addition operation, at least one amplification operation, and at least one delay operation.
5. The method for implementing zero phase by IIR filter according to claim 1, wherein the transfer function of the second filter is:
wherein ,c1 、c 2 、d 0 、d 1 、d 2 Is a coefficient of the second filter.
6. The method for realizing zero phase by using the IIR filter according to claim 1, wherein the first filter and the second filter are IIR filters.
7. An apparatus for implementing zero phase for an IIR filter, comprising a first filter and a second filter, the apparatus being configured to: the input signal is transmitted into the first filter for filtering, and a first signal is generated; the first signal is transmitted into the second filter for filtering, and a second signal is generated;
the phases of the first filter and the second filter are up and down symmetrical along the X axis;
the transfer function of the first filter is:
wherein a1= - (1-sin ω0+cos ω0)/(1+sin ω0+cos ω0);
a 2 = 0；
b 0 = sinω0 / (1+sinω0+cosω0)；
b 1 = sinω0 / (1+sinω0+cosω0)；
b 2 = 0，
wherein ,ω0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
8. The apparatus for implementing zero phase of an IIR filter of claim 7 wherein said first filter and second filter each comprise at least one adder, at least one amplifier, and at least one delay.
CN201910819813.6A 2019-08-31 2019-08-31 Method and device for realizing zero phase of IIR filter Active CN110601678B (en)

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US5089981A (en) * 1989-04-24 1992-02-18 Audio Precision, Inc. Hybrid form digital filter
CN101361650A (en) * 2007-08-07 2009-02-11 深圳市理邦精密仪器有限公司 Zero phase implementation method of IIR filter and zero phase IIR fiter

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GB2373385B (en) * 2001-03-13 2005-03-16 Ericsson Telefon Ab L M Radio receiver
EP1548940A1 (en) * 2003-12-18 2005-06-29 Harman Becker Automotive Systems GmbH Sample rate converter

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Publication number Priority date Publication date Assignee Title
US5089981A (en) * 1989-04-24 1992-02-18 Audio Precision, Inc. Hybrid form digital filter
CN101361650A (en) * 2007-08-07 2009-02-11 深圳市理邦精密仪器有限公司 Zero phase implementation method of IIR filter and zero phase IIR fiter

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